2.2.257 Problems 25601 to 25700

Table 2.527: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

25601

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{i t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.392

25602

\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.295

25603

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.261

25604

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{3 t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.311

25605

\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \\ \end{align*}

[[_linear, ‘class A‘]]

0.819

25606

\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} t \\ \end{align*}

[[_linear, ‘class A‘]]

1.837

25607

\begin{align*} -y+y^{\prime }&={\mathrm e}^{t} \cos \left (t \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

1.513

25608

\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.360

25609

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=t \,{\mathrm e}^{c t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.304

25610

\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} {\mathrm e}^{5 t} \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.103

25611

\begin{align*} y^{\prime \prime \prime \prime }-y&=t^{3} \cos \left (5 t \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.374

25612

\begin{align*} y^{\prime }-a y&=f \left (t \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

1.223

25613

\begin{align*} y^{\prime }-a y&={\mathrm e}^{c t} \\ \end{align*}

[[_linear, ‘class A‘]]

0.945

25614

\begin{align*} y^{\prime }-a y&={\mathrm e}^{i \omega t} \\ \end{align*}

[[_linear, ‘class A‘]]

1.710

25615

\begin{align*} y^{\prime }-a y&=t \\ \end{align*}

[[_linear, ‘class A‘]]

0.689

25616

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.244

25617

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.252

25618

\begin{align*} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{2 t} \\ \end{align*}

[[_2nd_order, _missing_y]]

0.798

25619

\begin{align*} y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\ \end{align*}

[[_2nd_order, _missing_y]]

0.782

25620

\begin{align*} y^{\prime \prime }+b y^{\prime }+c y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.307

25621

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.230

25622

\begin{align*} y^{\prime \prime }&=t \\ \end{align*}

[[_2nd_order, _quadrature]]

0.665

25623

\begin{align*} y^{\prime \prime }&=t^{2} \\ \end{align*}

[[_2nd_order, _quadrature]]

0.690

25624

\begin{align*} y^{\prime \prime }+y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.541

25625

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.223

25626

\begin{align*} \frac {c y^{\prime \prime }}{\omega ^{2}}+c y&=\cos \left (\omega t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.320

25627

\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.122

25628

\begin{align*} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.150

25629

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.072

25630

\begin{align*} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.105

25631

\begin{align*} y^{\prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ \end{align*}
Using Laplace transform method.

[_quadrature]

0.081

25632

\begin{align*} y^{\prime \prime }&={\mathrm e}^{a t} \\ y \left (0\right ) &= A \\ y^{\prime }\left (0\right ) &= B \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _quadrature]]

0.086

25633

\begin{align*} y^{\prime \prime }-y^{\prime }&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.097

25634

\begin{align*} y^{\prime \prime }+y&=\cos \left (\omega t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.115

25635

\begin{align*} y^{\prime \prime }+y&=\cos \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.107

25636

\begin{align*} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_linear, ‘class A‘]]

0.065

25637

\begin{align*} y^{\prime \prime }+a^{2} y&=1 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.126

25638

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.116

25639

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\delta \left (t \right ) \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.075

25640

\begin{align*} y^{\prime \prime }+y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.095

25641

\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _linear, _nonhomogeneous]]

0.109

25642

\begin{align*} y^{\prime \prime }+B y^{\prime }+C y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

[[_2nd_order, _missing_x]]

0.076

25643

\begin{align*} y^{\prime }&=-\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

[_quadrature]

0.095

25644

\begin{align*} y^{\prime }&=-\sin \left (t \right )+\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

[_quadrature]

0.094

25645

\begin{align*} y^{\prime }&=1-y^{2} \\ \end{align*}

[_quadrature]

1.315

25646

\begin{align*} y^{\prime }&=y^{2}-t \\ \end{align*}

[[_Riccati, _special]]

2.280

25647

\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\ \end{align*}

[_quadrature]

0.176

25648

\begin{align*} \left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

13.152

25649

\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}

[NONE]

0.041

25650

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.040

25651

\begin{align*} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \\ \end{align*}

[NONE]

0.273

25652

\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}

[[_2nd_order, _missing_x]]

1.716

25653

\begin{align*} R^{\prime \prime }&=-\frac {k}{R^{2}} \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

58.187

25654

\begin{align*} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.674

25655

\begin{align*} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

12.420

25656

\begin{align*} y^{2}-1+y^{\prime } x&=0 \\ \end{align*}

[_separable]

2.868

25657

\begin{align*} 2 y^{\prime }+y&=0 \\ \end{align*}

[_quadrature]

0.378

25658

\begin{align*} y^{\prime }+20 y&=24 \\ \end{align*}

[_quadrature]

0.313

25659

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.186

25660

\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.612

25661

\begin{align*} \left (y-x \right ) y^{\prime }&=y-x +8 \\ \end{align*}

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

0.947

25662

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

[_quadrature]

6.954

25663

\begin{align*} y^{\prime }&=2 x y^{2} \\ \end{align*}

[_separable]

2.488

25664

\begin{align*} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

3.517

25665

\begin{align*} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \\ \end{align*}

[_quadrature]

0.384

25666

\begin{align*} 2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

2.547

25667

\begin{align*} p^{\prime }&=p \left (1-p\right ) \\ \end{align*}

[_quadrature]

0.481

25668

\begin{align*} y^{\prime }+4 y x&=8 x^{3} \\ \end{align*}

[_linear]

2.217

25669

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.179

25670

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.234

25671

\begin{align*} y^{\prime } x -3 y x&=1 \\ \end{align*}

[[_linear, ‘class A‘]]

1.162

25672

\begin{align*} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \\ \end{align*}

[_linear]

1.957

25673

\begin{align*} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \\ \end{align*}

[_linear]

1.969

25674

\begin{align*} y^{\prime }+2 y x&=1 \\ \end{align*}

[_linear]

1.122

25675

\begin{align*} y^{\prime } x -2 y&=0 \\ \end{align*}

[_separable]

2.199

25676

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ \end{align*}

[_separable]

3.147

25677

\begin{align*} 2 y+y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.369

25678

\begin{align*} 3 y^{\prime }&=4 y \\ \end{align*}

[_quadrature]

0.354

25679

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.158

25680

\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.166

25681

\begin{align*} y^{\prime \prime } x +2 y^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.701

25682

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.911

25683

\begin{align*} 3 y^{\prime } x +5 y&=10 \\ \end{align*}

[_separable]

2.439

25684

\begin{align*} y^{\prime }&=y^{2}+2 y-3 \\ \end{align*}

[_quadrature]

0.318

25685

\begin{align*} \left (y-1\right ) y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.368

25686

\begin{align*} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.314

25687

\begin{align*} x^{\prime }&=x+3 y \\ y^{\prime }&=5 x+3 y \\ \end{align*}

system_of_ODEs

0.309

25688

\begin{align*} x^{\prime \prime }&=4 y+{\mathrm e}^{t} \\ y^{\prime \prime }&=4 x-{\mathrm e}^{t} \\ \end{align*}

system_of_ODEs

0.028

25689

\begin{align*} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.069

25690

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.101

25691

\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (0\right ) &= -{\frac {1}{3}} \\ \end{align*}

[_quadrature]

0.572

25692

\begin{align*} y^{\prime }&=y-y^{2} \\ y \left (-1\right ) &= 2 \\ \end{align*}

[_quadrature]

0.535

25693

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (2\right ) &= {\frac {1}{3}} \\ \end{align*}

[_separable]

2.822

25694

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (-2\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

2.811

25695

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.648

25696

\begin{align*} y^{\prime }+2 x y^{2}&=0 \\ y \left (\frac {1}{2}\right ) &= -4 \\ \end{align*}

[_separable]

2.874

25697

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= -1 \\ x^{\prime }\left (0\right ) &= 8 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.403

25698

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{2}\right ) &= 0 \\ x^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.486

25699

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{6}\right ) &= {\frac {1}{2}} \\ x^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.704

25700

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (\frac {\pi }{4}\right ) &= \sqrt {2} \\ x^{\prime }\left (\frac {\pi }{4}\right ) &= 2 \sqrt {2} \\ \end{align*}

[[_2nd_order, _missing_x]]

0.792